library(car)
## Loading required package: carData
library(emmeans)
dd<-read.csv2("Ficusdata.csv")
head(dd)
## Days H
## 1 4 7.4
## 2 4 5.9
## 3 4 4.9
## 4 4 6.1
## 5 4 5.9
## 6 4 5.4
Descriptive:
dd$FDays<-as.factor(dd$Days)
sp(H~Days, dd)
head(dd)
## Days H FDays
## 1 4 7.4 4
## 2 4 5.9 4
## 3 4 4.9 4
## 4 4 6.1 4
## 5 4 5.9 4
## 6 4 5.4 4
summary(m1<-lm(H~Days, dd))
##
## Call:
## lm(formula = H ~ Days, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.6952 -2.8803 -0.4206 2.9469 13.3749
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.456364 0.511898 -0.892 0.374
## Days 0.286780 0.006551 43.777 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.081 on 238 degrees of freedom
## Multiple R-squared: 0.8895, Adjusted R-squared: 0.8891
## F-statistic: 1916 on 1 and 238 DF, p-value: < 2.2e-16
plot(rstudent(m1),main="rstudent")
abline(h=c(-3,0,3),lty=2)
for (i in 1:length(rstudent(m1))){
if (rstudent(m1)[i] > 3) print(rstudent(m1)[i])
}
## 218
## 3.188103
## 230
## 3.188103
## 234
## 3.372391
leveneTest(resid(m1)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(m1)
summary(m1f<-lm(H~Days+FDays, dd))
##
## Call:
## lm(formula = H ~ Days + FDays, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.0333 -1.2708 -0.0333 1.3156 7.1667
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.119312 0.478106 8.616 1.13e-15 ***
## Days 0.299339 0.005199 57.580 < 2e-16 ***
## FDays18 -2.236574 0.621842 -3.597 0.000394 ***
## FDays32 -5.948148 0.595739 -9.984 < 2e-16 ***
## FDays46 -7.230556 0.577682 -12.516 < 2e-16 ***
## FDays60 -8.358796 0.568439 -14.705 < 2e-16 ***
## FDays74 -9.170370 0.568439 -16.133 < 2e-16 ***
## FDays88 -9.565278 0.577682 -16.558 < 2e-16 ***
## FDays102 -7.518519 0.595739 -12.620 < 2e-16 ***
## FDays116 -4.142593 0.621842 -6.662 1.97e-10 ***
## FDays130 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.269 on 230 degrees of freedom
## Multiple R-squared: 0.967, Adjusted R-squared: 0.9657
## F-statistic: 748.8 on 9 and 230 DF, p-value: < 2.2e-16
leveneTest(resid(m1f)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(m1f)
print(anova(m1, m1f))
## Analysis of Variance Table
##
## Model 1: H ~ Days
## Model 2: H ~ Days + FDays
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 238 3963.8
## 2 230 1184.2 8 2779.6 67.481 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
print(m1$coef[1]+m1$coef[2]*105)
## (Intercept)
## 29.65557
predict(m1)[105]
## 105
## 16.75045
emmeans(m1, ~Days)
## Days emmean SE df lower.CL upper.CL
## 67 18.75792 0.2634267 238 18.23897 19.27686
##
## Confidence level used: 0.95
Days2 <- dd$Days^2
summary(m2<-lm(H~Days+I(Days^2), dd))
##
## Call:
## lm(formula = H ~ Days + I(Days^2), data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.7770 -1.5422 -0.0596 1.3783 7.8653
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.2714174 0.4221346 14.856 <2e-16 ***
## Days -0.0271203 0.0146695 -1.849 0.0657 .
## I(Days^2) 0.0023425 0.0001058 22.133 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.335 on 237 degrees of freedom
## Multiple R-squared: 0.964, Adjusted R-squared: 0.9637
## F-statistic: 3171 on 2 and 237 DF, p-value: < 2.2e-16
summary(m2f<-lm(H~Days+I(Days^2)+FDays, dd))
##
## Call:
## lm(formula = H ~ Days + I(Days^2) + FDays, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.0333 -1.2708 -0.0333 1.3156 7.1667
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.4931311 0.5323630 10.318 < 2e-16 ***
## Days -0.0546840 0.0512325 -1.067 0.2869
## I(Days^2) 0.0026420 0.0003966 6.662 1.97e-10 ***
## FDays18 1.9060185 0.8298322 2.297 0.0225 *
## FDays32 1.3013889 1.1514892 1.130 0.2596
## FDays46 2.0902778 1.3906000 1.503 0.1342
## FDays60 1.9976852 1.4999794 1.332 0.1842
## FDays74 1.1861111 1.4687543 0.808 0.4202
## FDays88 -0.2444444 1.2974902 -0.188 0.8507
## FDays102 -0.2689815 1.0007401 -0.269 0.7883
## FDays116 NA NA NA NA
## FDays130 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.269 on 230 degrees of freedom
## Multiple R-squared: 0.967, Adjusted R-squared: 0.9657
## F-statistic: 748.8 on 9 and 230 DF, p-value: < 2.2e-16
anova(m2, m2f)
## Analysis of Variance Table
##
## Model 1: H ~ Days + I(Days^2)
## Model 2: H ~ Days + I(Days^2) + FDays
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 237 1292.4
## 2 230 1184.2 7 108.19 3.0018 0.004911 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(rstudent(m2),main="rstudent")
abline(h=c(-2,0,2),lty=2)
for (i in 1:length(rstudent(m2))){
if (rstudent(m2)[i] > 2) print(rstudent(m2)[i])
}
## 80
## 2.086828
## 200
## 2.775014
## 214
## 2.105581
## 218
## 3.167343
## 230
## 3.167343
## 234
## 3.492016
leveneTest(resid(m2)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(m2)
#summary(m2)
predict(m2, new=data.frame(Days=0), se.fit=TRUE)
## $fit
## 1
## 6.271417
##
## $se.fit
## [1] 0.4221346
##
## $df
## [1] 237
##
## $residual.scale
## [1] 2.335206
summary(m3<-lm(log(H)~Days, data = dd))
##
## Call:
## lm(formula = log(H) ~ Days, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57837 -0.07874 0.01515 0.09263 0.35401
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.585522 0.019688 80.53 <2e-16 ***
## Days 0.016732 0.000252 66.41 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.157 on 238 degrees of freedom
## Multiple R-squared: 0.9488, Adjusted R-squared: 0.9486
## F-statistic: 4410 on 1 and 238 DF, p-value: < 2.2e-16
plot(rstudent(m3),main="rstudent")
abline(h=c(-2,0,2),lty=2)
for (i in 1:length(rstudent(m3))){
if (rstudent(m3)[i] > 2) print(rstudent(m3)[i])
}
## 1
## 2.259143
## 31
## 2.145551
## 45
## 2.287293
## 80
## 2.185434
predict(m3, new=data.frame(Days=150), se.fit=TRUE)
## $fit
## 1
## 4.095349
##
## $se.fit
## [1] 0.02323702
##
## $df
## [1] 238
##
## $residual.scale
## [1] 0.1569562
leveneTest(resid(m3)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 4.9414 4.476e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(m3)
summary(m4<-lm(sqrt(H)~Days, data = dd))
##
## Call:
## lm(formula = sqrt(H) ~ Days, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.90381 -0.23459 -0.00804 0.24907 0.87420
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.8614427 0.0421684 44.14 <2e-16 ***
## Days 0.0334581 0.0005396 62.00 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3362 on 238 degrees of freedom
## Multiple R-squared: 0.9417, Adjusted R-squared: 0.9415
## F-statistic: 3844 on 1 and 238 DF, p-value: < 2.2e-16
predict(m4, new=data.frame(Days=150), se.fit=TRUE)
## $fit
## 1
## 6.880153
##
## $se.fit
## [1] 0.04977039
##
## $df
## [1] 238
##
## $residual.scale
## [1] 0.3361778
plot(rstudent(m4),main="rstudent")
abline(h=c(-2,0,2),lty=2)
for (i in 1:length(rstudent(m4))){
if (rstudent(m4)[i] > 2) print(rstudent(m4)[i])
}
## 1
## 2.189593
## 218
## 2.497858
## 230
## 2.497858
## 234
## 2.652342
leveneTest(resid(m4)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 1.1647 0.3187
## 230
plot(m4)
m3
##
## Call:
## lm(formula = log(H) ~ Days, data = dd)
##
## Coefficients:
## (Intercept) Days
## 1.58552 0.01673
summary(m5<-nls(H~exp(a+b*Days),start=list(a=1.58552,b=0.01673), data=dd))
##
## Formula: H ~ exp(a + b * Days)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## a 1.5985554 0.0276060 57.91 <2e-16 ***
## b 0.0166774 0.0002487 67.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.264 on 238 degrees of freedom
##
## Number of iterations to convergence: 2
## Achieved convergence tolerance: 9.882e-08
predict(m5, new=data.frame(Days=0), se.fit=TRUE)
## [1] 4.945883
leveneTest(resid(m5)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
a=1.58552
b=0.01673
print(exp(a + b * 0))
## [1] 4.881829
logLik(m1)
## 'log Lik.' -677.0625 (df=3)
logLik(m2)
## 'log Lik.' -542.5799 (df=4)
logLik(m3)
## 'log Lik.' 104.8882 (df=3)
logLik(m4)
## 'log Lik.' -77.91342 (df=3)
logLik(m5)
## 'log Lik.' -535.6415 (df=3)
AIC(m2, m3)
## df AIC
## m2 4 1093.1597
## m3 3 -203.7764
AIC(m2, m4)
## df AIC
## m2 4 1093.1597
## m4 3 161.8268
AIC(m2, m5)
## df AIC
## m2 4 1093.160
## m5 3 1077.283
summary(m1)
##
## Call:
## lm(formula = H ~ Days, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.6952 -2.8803 -0.4206 2.9469 13.3749
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.456364 0.511898 -0.892 0.374
## Days 0.286780 0.006551 43.777 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.081 on 238 degrees of freedom
## Multiple R-squared: 0.8895, Adjusted R-squared: 0.8891
## F-statistic: 1916 on 1 and 238 DF, p-value: < 2.2e-16
summary(m2)
##
## Call:
## lm(formula = H ~ Days + I(Days^2), data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.7770 -1.5422 -0.0596 1.3783 7.8653
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.2714174 0.4221346 14.856 <2e-16 ***
## Days -0.0271203 0.0146695 -1.849 0.0657 .
## I(Days^2) 0.0023425 0.0001058 22.133 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.335 on 237 degrees of freedom
## Multiple R-squared: 0.964, Adjusted R-squared: 0.9637
## F-statistic: 3171 on 2 and 237 DF, p-value: < 2.2e-16
summary(m3)
##
## Call:
## lm(formula = log(H) ~ Days, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57837 -0.07874 0.01515 0.09263 0.35401
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.585522 0.019688 80.53 <2e-16 ***
## Days 0.016732 0.000252 66.41 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.157 on 238 degrees of freedom
## Multiple R-squared: 0.9488, Adjusted R-squared: 0.9486
## F-statistic: 4410 on 1 and 238 DF, p-value: < 2.2e-16
summary(m4)
##
## Call:
## lm(formula = sqrt(H) ~ Days, data = dd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.90381 -0.23459 -0.00804 0.24907 0.87420
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.8614427 0.0421684 44.14 <2e-16 ***
## Days 0.0334581 0.0005396 62.00 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3362 on 238 degrees of freedom
## Multiple R-squared: 0.9417, Adjusted R-squared: 0.9415
## F-statistic: 3844 on 1 and 238 DF, p-value: < 2.2e-16
leveneTest(resid(m1)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(resid(m2)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(resid(m3)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 4.9414 4.476e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(resid(m4)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 1.1647 0.3187
## 230
leveneTest(resid(m5)~dd$FDays)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 9 5.099 2.699e-06 ***
## 230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
dias = 0
print(m1$coef[1]+m1$coef[2]*dias)
## (Intercept)
## -0.4563636
print(m2$coef[1]+m2$coef[2]*dias+m2$coef[3]*dias^2)
## (Intercept)
## 6.271417
print(exp(m3$coef[1]+m3$coef[2]*dias))
## (Intercept)
## 4.88184
print((m4$coef[1]+m4$coef[2]*dias)^2)
## (Intercept)
## 3.464969
a=1.58552
b=0.01673
print(exp(a + b * dias))
## [1] 4.881829
dias = 105
predict(m1, new=data.frame(Days=dias), se.fit=TRUE)[4]
## $residual.scale
## [1] 4.080989
predict(m2, new=data.frame(Days=dias), se.fit=TRUE)[4]
## $residual.scale
## [1] 2.335206
predict(m3, new=data.frame(Days=dias), se.fit=TRUE)[4]
## $residual.scale
## [1] 0.1569562
predict(m4, new=data.frame(Days=dias), se.fit=TRUE)[4]
## $residual.scale
## [1] 0.3361778
predict(m5, new=data.frame(Days=dias), se.fit=TRUE)[4]
## [1] NA
# 2.264